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Life History Evolution and the Origin of Multicellularity: the Case of Different Types of Cells

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Life History Evolution and the Origin of Multicellularity: the Case of Different Types of Cells Life history evolution and the origin of multicellularity: the case of different types of cells Fuad Aleskerov1 Denis Tverskoy2 Abstract The problem of unicellular-multicellular transition is one of the main issues that is discussing in evolutionary biology. In [1] the fitness of a colony of cells is considered in terms of its two basic components, viability and fecundity. Intrinsic trade-off function of each cell defines a type of cell. We elaborate models providing in [1]. Assuming that all intrinsic trade-off functions are linear, we construct a model with different cell types and show that the differentiation of these types tends to full specialization. In addition, we attempt to consider the fact that environmental factors influence on the fitness of the colony. Thus, we introduce an energy restriction to the model and show that in optimum we get situations in which there exists a set of states, each of them allowing colony to achieve the same maximum level of fitness. In some states arbitrary chosen cell may be specialized, in some – unspecialized, but fecundity and viability of each cell belong to limited ranges (which are unique for each cell). It is worth pointing out that the models from [1] are not robust. We try to overcome this disadvantage. Keywords: unicellular-multicellular transition, differentiation of types, energy constraints, germ- soma specialization, life-history evolution. 1. Introduction The problem of unicellular-multicellular transition is one of the main issues that is discussing in evolutionary biology. It is necessary to know how colonial organisms are transformed into multicellular organisms and what preconditions underlie this transition. The separation of a body's tissues is the main characteristic of a multicellular organism. This separation means that the majority of cells in the organism is specialized for one function and loses the potential ability to specialize for other functions. Some cells in a colonial organism may be specialized for specific functions but may not lose the ability to specialize elsewhere. If conditions that lead the colony to full specialization are performed over a long period of time, it is possible that the unicellular-multicellular transition will occur. Therefore, it is important to determine the conditions that contribute to the full specialization of a colonial organism. For example, it is reasonable to suspect that different cell types may cause full specialization. Another interesting question is the influence of [email protected], International Laboratory for Decision Analysis and Choice and Department of Mathematics for Economics of the National Research University Higher School of Economics (NRU HSE), and Institute of Control Sciences of Russian Academy of Sciences [email protected],International Laboratory for Decision Analysis and Choice and Department of Mathematics for Economics of the National Research University Higher School of Economics (NRU HSE), and Institute of Control Sciences of Russian Academy of Sciences 1 environmental factors on the colony's behavior. We introduce these environmental factors into the model in the form of the total energy constraints consumed by considering colony of cells. Fundamental models investigated the problem of unicellular – multicellular transition were provided in [1]. These models best illustrate evolution of Volvocalean Green Algae but they may be applied to other lineages as well. In [1] the model has been illustrated on the example of volvocales green algae. These are flagellated photosynthetic organisms with coherent glycoprotein cell walls and represent the most appropriate system in research of the process of transition under study, because Volvocales linage ranges from the single-cell organisms to undifferentiated, soma-differentiated and germ-soma differentiated organisms arranged according to the size of the colony. Volvocales live in standing waters and so need flagellar beating in order to move toward light and nutrients. Therefore motility is an important factor contributing to viability of Volvocales [2]. Volvocales’ type of cell division represents palintomy with multiple fission. Also, useful fact is that the species with increased cell specialization do not have a single origin. However, the results in [1] look non-robust. Because of the identity of all cells in the colony assumed in [1], in optimum it does not matter which cells belong to the sets of soma-specialized cells or germ-specialized cells. So, if we change slightly some characteristics that not reflected explicitly in the model, sets of germ and soma-specialized cells changes – the model only requires that the ratio between their cardinality should remain constant. Thus, small changes in parameters may force soma-specialized cell become germ-specialized immediately. In linear case this non-robustness also lies in a fact that no more than the half cells can be soma- specialized and no more than the half cells can be germ-specialized. These facts have attracted our attention and we provide a new model to overcome above mentioned non-robustness of this beautiful model developed in [1]. Structure of the text. We begin with the model, provided in [1] and describe it in Section 2. Then in Section 3 we propose the model with different cell types, extend this model taking into account energy constraints in Section 4. In section 5 we give a short survey of related works. Section 6 concludes. 2. An overview of the models In [1], the authors constructed models that explore the fitness trade-offs at both the cell and group levels during the unicellular-multicellular transition. Thus, fitness is considered in terms of its two basic components: viability and fecundity. In [1], the trade-off function (1) is studied, which reflects the intrinsic relationships that link viability and fecundity within the cell due to cell physiology and other constraints. Let v be viability and b represents fecundity. Then: 2 In [1], the authors noted that in unicellular organisms, the cell must contribute to both of the fitness components. In multicellular groups, each cell may be unspecialized, such as in unicellular organisms, or, in contrast, may specialize only in the germ or only in the soma. This fact can lead to the formation of germ – soma (“G-S”) specialization, in which some cells lose their autonomy in favor of the group and, as a result, their fitness and individuality are transferred from the cell level to the group level. In [1], the cases in which “G-S” specialization may occur are studied. It is noted as well that the models are most applicable to volvocine green algae. There are two types of models that are considered in [1]: the fitness isocline model and the full optimization model. We discuss only the second model because this model is more general than the fitness isocline model. In the full optimization model, all of the cells are considered simultaneously, and the strategic purpose of the colony is to maximize its fitness. Below, we describe this model in detail to emphasize its advantages and disadvantages. Then we try to improve it. 2.1. Full optimization model Consider a colony consisting of N cells, are indices of cells in the colony, – resulting contribution of cell i to the fecundity of the group, – viability-enhancing capability of cell i. The fitness trade-off function (continuous and determined on a convex hull) is more common than a linear function and should be the same for all of the cells from the colony: The group’s level of fecundity is an additive function of variable bi. The group’s level of viability is an additive function of variable vi, i.e., In [1], it is assumed that the group fitness, which we should maximize, is the product of the group viability and fecundity: In [1], the problem of choosing the correct form of the group fitness function is also discussed. This type of function (4) is based on simple intuition. For instance, imagine that one cell in the group has a high level of fecundity but low viability, and another cell is strictly the opposite, with a high level of viability and low fecundity. Each of these cells by itself would have a low fitness, but together they can achieve a high fitness for the group. Function (4) considers this reasoning in contrast to, for example, the average fitness of all cells (5): 3 However, we should note that most of the assumptions in [1] would still hold even if the fitness is described by a more general function with special properties. In general, the full optimization model can be written formally as a type of optimization problem (6): Assume that there is no initial cost of reproduction in the model. In this case, the following results are true: 1. If the function is strictly concave, then the group of cells should remain unspecialized. 2. If the function is linear , then the group of cells behaves as if there was just one cell; therefore, each cell is indifferent to specialization. 3. If the function is strictly convex, then the group of cells aims for full specialization. In addition, if there is an even number of cells in the group, then half should specialize in the germ and a half in the soma. If there is an odd number of cells in the group, of these cells should specialize in the germ, should specialize in the soma and one cell should remain unspecialized. An initial investment is necessary for reproduction. This investment requires an additional spending of energy, which can lead to the appearance of initial costs of reproduction that can be considered within the trade-off function. The initial costs of reproduction lead to full specialization in linear and convex cases of improved model and provide the opportunity for specialization in the concave case of this model. Despite all of the fundamental results of the full optimization model, there are a wide variety of problems that cannot be solved using this model and some disadvantages that are connected strictly with biological processes that this model cannot describe.
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